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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/vector_fe/vector_fe_ex6" target="_blank">Open vector_fe_ex6 in new tab.</a>
<a name="output"></a>
<br><br><br> <h1> The console output of the program: </h1>
<pre>
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=TRI6 boundary_condition=neumann
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=961
    n_local_nodes()=961
  n_elem()=450
    n_local_elem()=450
    n_active_elem()=450
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p" "l"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
    Approximation Orders="FIRST" "CONSTANT" "FIRST"
    n_dofs()=1156
    n_local_dofs()=1156
    max(n_local_dofs())=1156
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=1156
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.66955
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 1156
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.134373
HDiv semi-norm error is: 0.344042
HDiv error is: 0.369353
~~ Scalar field (p) ~~
L2 error is: 0.0697863

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=TRI6 boundary_condition=neumann
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=TRI7 boundary_condition=neumann
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={THIRD}
  supported_nodal_order()=3
  spatial_dimension()=2
  n_nodes()=1411
    n_local_nodes()=1411
  n_elem()=450
    n_local_elem()=450
    n_active_elem()=450
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p" "l"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
    Approximation Orders="FIRST" "CONSTANT" "FIRST"
    n_dofs()=1156
    n_local_dofs()=1156
    max(n_local_dofs())=1156
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=1156
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.66955
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 1156
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.134373
HDiv semi-norm error is: 0.344042
HDiv error is: 0.369353
~~ Scalar field (p) ~~
L2 error is: 0.0697863

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=TRI7 boundary_condition=neumann
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=QUAD8 boundary_condition=neumann
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=736
    n_local_nodes()=736
  n_elem()=225
    n_local_elem()=225
    n_active_elem()=225
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p" "l"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
    Approximation Orders="FIRST" "CONSTANT" "FIRST"
    n_dofs()=706
    n_local_dofs()=706
    max(n_local_dofs())=706
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=706
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 9.3711
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 706
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.134503
HDiv semi-norm error is: 0.421249
HDiv error is: 0.442201
~~ Scalar field (p) ~~
L2 error is: 0.0854505

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=QUAD8 boundary_condition=neumann
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=QUAD9 boundary_condition=neumann
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=961
    n_local_nodes()=961
  n_elem()=225
    n_local_elem()=225
    n_active_elem()=225
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p" "l"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
    Approximation Orders="FIRST" "CONSTANT" "FIRST"
    n_dofs()=706
    n_local_dofs()=706
    max(n_local_dofs())=706
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=706
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 9.3711
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 706
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.134503
HDiv semi-norm error is: 0.421249
HDiv error is: 0.442201
~~ Scalar field (p) ~~
L2 error is: 0.0854505

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=QUAD9 boundary_condition=neumann
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=TRI6 boundary_condition=neumann
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=961
    n_local_nodes()=961
  n_elem()=450
    n_local_elem()=450
    n_active_elem()=450
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p" "l"
    Finite Element Types="RAVIART_THOMAS" "L2_HIERARCHIC" "SCALAR"
    Approximation Orders="SECOND" "FIRST" "FIRST"
    n_dofs()=3661
    n_local_dofs()=3661
    max(n_local_dofs())=3661
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=3661
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 16.168
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 3661
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.00401719
HDiv semi-norm error is: 0.0139513
HDiv error is: 0.0145182
~~ Scalar field (p) ~~
L2 error is: 0.00282793

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=TRI6 boundary_condition=neumann
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=TRI7 boundary_condition=neumann
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={THIRD}
  supported_nodal_order()=3
  spatial_dimension()=2
  n_nodes()=1411
    n_local_nodes()=1411
  n_elem()=450
    n_local_elem()=450
    n_active_elem()=450
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p" "l"
    Finite Element Types="RAVIART_THOMAS" "L2_HIERARCHIC" "SCALAR"
    Approximation Orders="SECOND" "FIRST" "FIRST"
    n_dofs()=3661
    n_local_dofs()=3661
    max(n_local_dofs())=3661
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=3661
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 16.168
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 3661
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.00401719
HDiv semi-norm error is: 0.0139513
HDiv error is: 0.0145182
~~ Scalar field (p) ~~
L2 error is: 0.00282793

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=TRI7 boundary_condition=neumann
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=QUAD8 boundary_condition=neumann
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=736
    n_local_nodes()=736
  n_elem()=225
    n_local_elem()=225
    n_active_elem()=225
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p" "l"
    Finite Element Types="RAVIART_THOMAS" "L2_HIERARCHIC" "SCALAR"
    Approximation Orders="SECOND" "FIRST" "FIRST"
    n_dofs()=2761
    n_local_dofs()=2761
    max(n_local_dofs())=2761
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=2761
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 22.2532
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 2761
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.00363112
HDiv semi-norm error is: 0.0114015
HDiv error is: 0.0119658
~~ Scalar field (p) ~~
L2 error is: 0.00231062

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=QUAD8 boundary_condition=neumann
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=QUAD9 boundary_condition=neumann
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=961
    n_local_nodes()=961
  n_elem()=225
    n_local_elem()=225
    n_active_elem()=225
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p" "l"
    Finite Element Types="RAVIART_THOMAS" "L2_HIERARCHIC" "SCALAR"
    Approximation Orders="SECOND" "FIRST" "FIRST"
    n_dofs()=2761
    n_local_dofs()=2761
    max(n_local_dofs())=2761
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=2761
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 22.2532
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 2761
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.00363112
HDiv semi-norm error is: 0.0114015
HDiv error is: 0.0119658
~~ Scalar field (p) ~~
L2 error is: 0.00231062

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=QUAD9 boundary_condition=neumann
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=3 element_type=TET14 boundary_condition=neumann grid_size=6
***************************************************************

 Mesh Information:
  elem_dimensions()={3}
  elem_default_orders()={THIRD}
  supported_nodal_order()=3
  spatial_dimension()=3
  n_nodes()=19045
    n_local_nodes()=19045
  n_elem()=5184
    n_local_elem()=5184
    n_active_elem()=5184
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p" "l"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
    Approximation Orders="FIRST" "CONSTANT" "FIRST"
    n_dofs()=15985
    n_local_dofs()=15985
    max(n_local_dofs())=15985
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=15985
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 9.48596
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 15985
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.33477
HDiv semi-norm error is: 0.836328
HDiv error is: 0.900841
~~ Scalar field (p) ~~
L2 error is: 0.113076

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=3 element_type=TET14 boundary_condition=neumann grid_size=6
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=3 element_type=HEX27 boundary_condition=neumann
***************************************************************

 Mesh Information:
  elem_dimensions()={3}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=3
  n_nodes()=29791
    n_local_nodes()=29791
  n_elem()=3375
    n_local_elem()=3375
    n_active_elem()=3375
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p" "l"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL" "SCALAR"
    Approximation Orders="FIRST" "CONSTANT" "FIRST"
    n_dofs()=14176
    n_local_dofs()=14176
    max(n_local_dofs())=14176
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=14176
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 12.9992
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 14176
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.2325
HDiv semi-norm error is: 0.773177
HDiv error is: 0.807378
~~ Scalar field (p) ~~
L2 error is: 0.104528

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=3 element_type=HEX27 boundary_condition=neumann
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=TRI6 boundary_condition=dirichlet
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=961
    n_local_nodes()=961
  n_elem()=450
    n_local_elem()=450
    n_active_elem()=450
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
    Approximation Orders="FIRST" "CONSTANT"
    n_dofs()=1155
    n_local_dofs()=1155
    max(n_local_dofs())=1155
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=1155
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 5.67532
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 7
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.134279
HDiv semi-norm error is: 0.344042
HDiv error is: 0.369318
~~ Scalar field (p) ~~
L2 error is: 0.0697398

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=TRI6 boundary_condition=dirichlet
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=TRI7 boundary_condition=dirichlet
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={THIRD}
  supported_nodal_order()=3
  spatial_dimension()=2
  n_nodes()=1411
    n_local_nodes()=1411
  n_elem()=450
    n_local_elem()=450
    n_active_elem()=450
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
    Approximation Orders="FIRST" "CONSTANT"
    n_dofs()=1155
    n_local_dofs()=1155
    max(n_local_dofs())=1155
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=1155
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 5.67532
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 7
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.134279
HDiv semi-norm error is: 0.344042
HDiv error is: 0.369318
~~ Scalar field (p) ~~
L2 error is: 0.0697398

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=TRI7 boundary_condition=dirichlet
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=QUAD8 boundary_condition=dirichlet
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=736
    n_local_nodes()=736
  n_elem()=225
    n_local_elem()=225
    n_active_elem()=225
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
    Approximation Orders="FIRST" "CONSTANT"
    n_dofs()=705
    n_local_dofs()=705
    max(n_local_dofs())=705
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=705
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.38298
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 9
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.134333
HDiv semi-norm error is: 0.421249
HDiv error is: 0.442149
~~ Scalar field (p) ~~
L2 error is: 0.0853821

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=QUAD8 boundary_condition=dirichlet
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=QUAD9 boundary_condition=dirichlet
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=961
    n_local_nodes()=961
  n_elem()=225
    n_local_elem()=225
    n_active_elem()=225
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
    Approximation Orders="FIRST" "CONSTANT"
    n_dofs()=705
    n_local_dofs()=705
    max(n_local_dofs())=705
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=705
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.38298
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 9
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.134333
HDiv semi-norm error is: 0.421249
HDiv error is: 0.442149
~~ Scalar field (p) ~~
L2 error is: 0.0853821

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 element_type=QUAD9 boundary_condition=dirichlet
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=TRI6 boundary_condition=dirichlet
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=961
    n_local_nodes()=961
  n_elem()=450
    n_local_elem()=450
    n_active_elem()=450
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p"
    Finite Element Types="RAVIART_THOMAS" "L2_HIERARCHIC"
    Approximation Orders="SECOND" "FIRST"
    n_dofs()=3660
    n_local_dofs()=3660
    max(n_local_dofs())=3660
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=3660
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 14.1721
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 20
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.00399517
HDiv semi-norm error is: 0.0139513
HDiv error is: 0.0145121
~~ Scalar field (p) ~~
L2 error is: 0.00282792

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=TRI6 boundary_condition=dirichlet
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=TRI7 boundary_condition=dirichlet
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={THIRD}
  supported_nodal_order()=3
  spatial_dimension()=2
  n_nodes()=1411
    n_local_nodes()=1411
  n_elem()=450
    n_local_elem()=450
    n_active_elem()=450
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p"
    Finite Element Types="RAVIART_THOMAS" "L2_HIERARCHIC"
    Approximation Orders="SECOND" "FIRST"
    n_dofs()=3660
    n_local_dofs()=3660
    max(n_local_dofs())=3660
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=3660
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 14.1721
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 20
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.00399517
HDiv semi-norm error is: 0.0139513
HDiv error is: 0.0145121
~~ Scalar field (p) ~~
L2 error is: 0.00282792

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=TRI7 boundary_condition=dirichlet
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=QUAD8 boundary_condition=dirichlet
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=736
    n_local_nodes()=736
  n_elem()=225
    n_local_elem()=225
    n_active_elem()=225
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p"
    Finite Element Types="RAVIART_THOMAS" "L2_HIERARCHIC"
    Approximation Orders="SECOND" "FIRST"
    n_dofs()=2760
    n_local_dofs()=2760
    max(n_local_dofs())=2760
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=2760
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 20.2609
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 30
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.00363112
HDiv semi-norm error is: 0.0114015
HDiv error is: 0.0119658
~~ Scalar field (p) ~~
L2 error is: 0.00231062

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=QUAD8 boundary_condition=dirichlet
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=QUAD9 boundary_condition=dirichlet
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=2
  n_nodes()=961
    n_local_nodes()=961
  n_elem()=225
    n_local_elem()=225
    n_active_elem()=225
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p"
    Finite Element Types="RAVIART_THOMAS" "L2_HIERARCHIC"
    Approximation Orders="SECOND" "FIRST"
    n_dofs()=2760
    n_local_dofs()=2760
    max(n_local_dofs())=2760
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=2760
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 20.2609
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 30
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.00363112
HDiv semi-norm error is: 0.0114015
HDiv error is: 0.0119658
~~ Scalar field (p) ~~
L2 error is: 0.00231062

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=2 order=2 element_type=QUAD9 boundary_condition=dirichlet
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=3 element_type=TET14 boundary_condition=dirichlet grid_size=6
***************************************************************

 Mesh Information:
  elem_dimensions()={3}
  elem_default_orders()={THIRD}
  supported_nodal_order()=3
  spatial_dimension()=3
  n_nodes()=19045
    n_local_nodes()=19045
  n_elem()=5184
    n_local_elem()=5184
    n_active_elem()=5184
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
    Approximation Orders="FIRST" "CONSTANT"
    n_dofs()=15984
    n_local_dofs()=15984
    max(n_local_dofs())=15984
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=15984
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 7.48649
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 9
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.334729
HDiv semi-norm error is: 0.836328
HDiv error is: 0.900826
~~ Scalar field (p) ~~
L2 error is: 0.113055

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=3 element_type=TET14 boundary_condition=dirichlet grid_size=6
***************************************************************
***************************************************************
* Running Example vector_fe_ex6:
*   ./example-opt dim=3 element_type=HEX27 boundary_condition=dirichlet
***************************************************************

 Mesh Information:
  elem_dimensions()={3}
  elem_default_orders()={SECOND}
  supported_nodal_order()=2
  spatial_dimension()=3
  n_nodes()=29791
    n_local_nodes()=29791
  n_elem()=3375
    n_local_elem()=3375
    n_active_elem()=3375
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "DivGrad"
    Type "LinearImplicit"
    Variables="u" "p"
    Finite Element Types="RAVIART_THOMAS" "MONOMIAL"
    Approximation Orders="FIRST" "CONSTANT"
    n_dofs()=14175
    n_local_dofs()=14175
    max(n_local_dofs())=14175
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=14175
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 11
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 13
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

~~ Vector field (u) ~~
L2 error is: 0.23237
HDiv semi-norm error is: 0.773177
HDiv error is: 0.807341
~~ Scalar field (p) ~~
L2 error is: 0.104476

***************************************************************
* Done Running Example vector_fe_ex6:
*   ./example-opt dim=3 element_type=HEX27 boundary_condition=dirichlet
***************************************************************
</pre>
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